Growth and decay

Simple interest (Foundation)

Linear growth: interest is calculated on the original amount only.

Formula: I = (P × R × T) / 100, where P = principal, R = rate (% per year), T = time (years).

Total at end = P + I.

Compound interest (both tiers; Higher uses formula)

Each year's interest is added to the principal, so next year's interest is on the new total. This is exponential growth.

Formula: A = P × (1 + r/100)ⁿ

• A = final amount
• P = principal (starting amount)
• r = annual rate as a percentage
• n = number of years

Example: £2000 at 4% for 3 years. A = 2000 × 1.04³ = 2000 × 1.124864 = £2249.73.

Compound depreciation

Same formula but with a minus sign: A = P × (1 − r/100)ⁿ.

Example: a car worth £15,000 depreciates at 12% per year. After 4 years: A = 15000 × 0.88⁴ = 15000 × 0.5997 = £8995.21.

General exponential model

y = a × bˣ

• a = initial value
• b = growth (b > 1) or decay factor (0 < b < 1)
• x = number of time periods

If a percentage growth rate r% is given, b = 1 + r/100. If decay r%, b = 1 − r/100.

Word problems

Watch for the time period — sometimes "monthly" or "quarterly" rather than annually. Convert if needed (rare on CCEA Foundation).

Population growing at 3% per year, currently 50,000: After 5 years: 50000 × 1.03⁵ = 57,963 (rounded).

Common CCEA exam tip

The compound formula is on the CCEA formula sheet for Higher tier. Always state the substitution clearly: A = 2000 × (1.04)³ scores M1 even before evaluating.